Most people are only familiar with a handful of numbers that can’t be written as fractions, like $latex sqrt{2}$ or $latex pi$. But such numbers, called irrational numbers, are far more plentiful than fractions or rational numbers. How easy are they to approximate with fractions? If you use a fraction with an arbitrarily large denominator, you can get arbitrarily close. (As is well known, 22/7...